On asymptotic behavior of the mass of rays

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6 Citations (Scopus)


We consider the measure of the set of all unit vectors tangent to rays emanating from a point p in a finitely connected complete open Riemannian 2-manifold M. If M with one end admits total curvature c(M), then this measure tends to min(2πx(M)-c(M), 2π) as p tends to infinity, where x(M) is the Euler characteristic.

Original languageEnglish
Pages (from-to)495-505
Number of pages11
JournalProceedings of the American Mathematical Society
Issue number2
Publication statusPublished - 1990 Feb


  • Complete open manifolds
  • Gauss-Bonnet theorem
  • Geodesies
  • Rays
  • Total curvature


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